Fast Memory-Efficient Generalized Belief Propagation

1
Fast Memory-Efficient Generalized Belief
Propagation
M.Pawan Kumar P.H.S. Torr Oxford Brookes University, UK

Aim To reduce time and memory requirements of
Generalized Belief
Propagation.
Results
Fast LBP
Message M max xi ?(xi,xj) Local Belief (xi)

• 100 random MRFs for varying nC/nL

Highest LB Label
Belief Propagation
nC
nC
OR

• Sites of MRF are clustered into regions.
• Regions pass messages to subregions until
  convergence.

ij
j
ij
j
ij
j
Time
Memory
Fast GBP
Message M max xi ?(xi,xj) ?(xi,xj)
LB(xi,xj) LB(xi,xk)
Loopy Belief Propagation (LBP)
Subgraph Matching

• Regions of size 2
• Inaccurate Bethe approximation
• Computationally inexpensive

nC
ijk
jk
nC
T1
ijk
jk
OR
G2 (V2,E2)
G1 (V1,E1)
MRF
MRF
Regions Messages
Highest LB(xi,xj) Label

• 1000 synthetic pairs of graphs
• 7 noise added

Generalized Belief Propagation (GBP)

ij
j
ik
k
Highest LB(xi,xk) Label
T3
T2

• Regions of arbitrary size S
• Accurate Kikuchi approximation
• Computationally expensive

Method Time Memory Accuracy
LBP 2 sec 4 MB 78.61
GBP - gt 350 MB -
Efficient LBP 0.2 sec 0.4 MB 78.61
Efficient GBP 4.3 sec 3.5 MB 95.79

• The same label xi of site i is used to computed
  the terms T2 and T3.

Proof in paper.

• Term T1 takes O(nL/nC) less time than message M.

Memory-Efficient GBP
Truncation Factor 0
MRF
Regions Messages
Robust Truncated Model (RTM)
Do not contribute to message
Object Recognition
nL
Outline
nC
nC
nC
Texture
P
Q
P
Q

• Divide MRF into smaller MRFs which can be solved
  one at a time.

Part likelihood
Spatial Prior

• Number of stored messages reduced by
  O((nL/nC)S-1).

A
B
Bipartite Graphs
Pairwise Potentials ?(xi,xj)

• Time 16 sec. Memory 0.5 MB

Model Time Memory
RTM O(nL/nC)
Truncation 0 O(nL/nC) O((nL/nC) S-1)
Bipartite Graphs Half
ROC Curves - 450 ve and 2400 -ve images
A
B
Regions
MRF

• Message within A depends only on messages from B
  (and vice versa).

Reduction in Time and Memory Requirements

• Number of stored messages can be halved.